Math Problem Statement
Given the following notations, write a formula for x, the break-even sales level. SP = selling price per unit FC = total fixed cost VC = variable cost per unit x =
Solution
The break-even sales level is the point where total revenue equals total costs. Using the given notations:
- = selling price per unit,
- = total fixed cost,
- = variable cost per unit,
- = number of units sold (break-even point).
Formula for the break-even point:
At the break-even point:
Total Revenue is:
Total Costs are the sum of fixed costs and variable costs:
Setting the two equal to each other:
Now, solve for :
Thus, the break-even sales level is:
This is the formula for the break-even sales level.
Would you like any further explanation or details on how this formula works?
Here are 5 related questions:
- How do changes in the selling price affect the break-even point?
- What happens to the break-even point if the variable cost per unit increases?
- Can you calculate the break-even sales level if given specific values for SP, VC, and FC?
- How does the break-even formula adjust for multiple products with different prices and costs?
- What is the relationship between contribution margin and the break-even point?
Tip: Always ensure that the selling price is greater than the variable cost; otherwise, the business will incur a loss for each unit sold.
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Math Problem Analysis
Mathematical Concepts
Algebra
Break-even analysis
Linear equations
Formulas
Break-even formula: x = FC / (SP - VC)
Theorems
Break-even point theory
Suitable Grade Level
Grades 9-12
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